<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.9.1"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Eigen-unsupported: LMqrsolv.h Source File</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="resize.js"></script>
<script type="text/javascript" src="navtreedata.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/searchdata.js"></script>
<script type="text/javascript" src="search/search.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
  $(document).ready(function() { init_search(); });
/* @license-end */
</script>
<script type="text/x-mathjax-config">
  MathJax.Hub.Config({
    extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
    jax: ["input/TeX","output/HTML-CSS"],
});
</script>
<script type="text/javascript" async="async" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js"></script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
<link href="eigendoxy.css" rel="stylesheet" type="text/css">
<!--  -->
<script type="text/javascript" src="eigen_navtree_hacks.js"></script>
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
 <tbody>
 <tr style="height: 56px;">
  <td id="projectlogo"><img alt="Logo" src="Eigen_Silly_Professor_64x64.png"/></td>
  <td id="projectalign" style="padding-left: 0.5em;">
   <div id="projectname"><a href="http://eigen.tuxfamily.org">Eigen-unsupported</a>
   &#160;<span id="projectnumber">3.4.90 (git rev 67eeba6e720c5745abc77ae6c92ce0a44aa7b7ae)</span>
   </div>
  </td>
   <td>        <div id="MSearchBox" class="MSearchBoxInactive">
        <span class="left">
          <img id="MSearchSelect" src="search/mag_sel.svg"
               onmouseover="return searchBox.OnSearchSelectShow()"
               onmouseout="return searchBox.OnSearchSelectHide()"
               alt=""/>
          <input type="text" id="MSearchField" value="Search" accesskey="S"
               onfocus="searchBox.OnSearchFieldFocus(true)" 
               onblur="searchBox.OnSearchFieldFocus(false)" 
               onkeyup="searchBox.OnSearchFieldChange(event)"/>
          </span><span class="right">
            <a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.svg" alt=""/></a>
          </span>
        </div>
</td>
 </tr>
 </tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.9.1 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
var searchBox = new SearchBox("searchBox", "search",false,'Search','.html');
/* @license-end */
</script>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
  <div id="nav-tree">
    <div id="nav-tree-contents">
      <div id="nav-sync" class="sync"></div>
    </div>
  </div>
  <div id="splitbar" style="-moz-user-select:none;" 
       class="ui-resizable-handle">
  </div>
</div>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
$(document).ready(function(){initNavTree('LMqrsolv_8h_source.html',''); initResizable(); });
/* @license-end */
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
     onmouseover="return searchBox.OnSearchSelectShow()"
     onmouseout="return searchBox.OnSearchSelectHide()"
     onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>

<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0" 
        name="MSearchResults" id="MSearchResults">
</iframe>
</div>

<div class="header">
  <div class="headertitle">
<div class="title">LMqrsolv.h</div>  </div>
</div><!--header-->
<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2009 Thomas Capricelli &lt;orzel@freehackers.org&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2012 Desire Nuentsa &lt;desire.nuentsa_wakam@inria.fr&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// This code initially comes from MINPACK whose original authors are:</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// Copyright Jorge More - Argonne National Laboratory</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// Copyright Burt Garbow - Argonne National Laboratory</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">// Copyright Ken Hillstrom - Argonne National Laboratory</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Minpack license</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment">// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; </div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="preprocessor">#ifndef EIGEN_LMQRSOLV_H</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#define EIGEN_LMQRSOLV_H</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160; </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160; </div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> { </div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160; </div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160; </div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar,<span class="keywordtype">int</span> Rows, <span class="keywordtype">int</span> Cols, <span class="keyword">typename</span> PermIndex&gt;</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="keywordtype">void</span> lmqrsolv(</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;  Matrix&lt;Scalar,Rows,Cols&gt; &amp;s,</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;  <span class="keyword">const</span> PermutationMatrix&lt;Dynamic,Dynamic,PermIndex&gt; &amp;iPerm,</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;  <span class="keyword">const</span> <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt;Scalar,Dynamic,1&gt;</a> &amp;diag,</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;  <span class="keyword">const</span> <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt;Scalar,Dynamic,1&gt;</a> &amp;qtb,</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;  <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt;Scalar,Dynamic,1&gt;</a> &amp;x,</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;  <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt;Scalar,Dynamic,1&gt;</a> &amp;sdiag)</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;{</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <span class="comment">/* Local variables */</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i, j, k;</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    Scalar temp;</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = s.cols();</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt;Scalar,Dynamic,1&gt;</a>  wa(n);</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    JacobiRotation&lt;Scalar&gt; givens;</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160; </div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    <span class="comment">/* Function Body */</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="comment">// the following will only change the lower triangular part of s, including</span></div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    <span class="comment">// the diagonal, though the diagonal is restored afterward</span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160; </div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    <span class="comment">/*     copy r and (q transpose)*b to preserve input and initialize s. */</span></div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    <span class="comment">/*     in particular, save the diagonal elements of r in x. */</span></div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    x = s.diagonal();</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;    wa = qtb;</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    </div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;   </div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;    s.topLeftCorner(n,n).template triangularView&lt;StrictlyLower&gt;() = s.topLeftCorner(n,n).transpose();</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    <span class="comment">/*     eliminate the diagonal matrix d using a givens rotation. */</span></div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    <span class="keywordflow">for</span> (j = 0; j &lt; n; ++j) {</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160; </div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;        <span class="comment">/*        prepare the row of d to be eliminated, locating the */</span></div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;        <span class="comment">/*        diagonal element using p from the qr factorization. */</span></div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;        <span class="keyword">const</span> PermIndex l = iPerm.indices()(j);</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;        <span class="keywordflow">if</span> (diag[l] == 0.)</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;            <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        sdiag.tail(n-j).<a class="codeRef" href="../classEigen_1_1PlainObjectBase.html#acc39eaf7ba22b725c86f1b9b8bb57c3c">setZero</a>();</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;        sdiag[j] = diag[l];</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160; </div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        <span class="comment">/*        the transformations to eliminate the row of d */</span></div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;        <span class="comment">/*        modify only a single element of (q transpose)*b */</span></div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        <span class="comment">/*        beyond the first n, which is initially zero. */</span></div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        Scalar qtbpj = 0.;</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;        <span class="keywordflow">for</span> (k = j; k &lt; n; ++k) {</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;            <span class="comment">/*           determine a givens rotation which eliminates the */</span></div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;            <span class="comment">/*           appropriate element in the current row of d. */</span></div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;            givens.makeGivens(-s(k,k), sdiag[k]);</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160; </div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;            <span class="comment">/*           compute the modified diagonal element of r and */</span></div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;            <span class="comment">/*           the modified element of ((q transpose)*b,0). */</span></div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;            s(k,k) = givens.c() * s(k,k) + givens.s() * sdiag[k];</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;            temp = givens.c() * wa[k] + givens.s() * qtbpj;</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;            qtbpj = -givens.s() * wa[k] + givens.c() * qtbpj;</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;            wa[k] = temp;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160; </div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;            <span class="comment">/*           accumulate the transformation in the row of s. */</span></div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;            <span class="keywordflow">for</span> (i = k+1; i&lt;n; ++i) {</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;                temp = givens.c() * s(i,k) + givens.s() * sdiag[i];</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;                sdiag[i] = -givens.s() * s(i,k) + givens.c() * sdiag[i];</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;                s(i,k) = temp;</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;            }</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;        }</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    }</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;  </div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    <span class="comment">/*     solve the triangular system for z. if the system is */</span></div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <span class="comment">/*     singular, then obtain a least squares solution. */</span></div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> nsing;</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    <span class="keywordflow">for</span>(nsing=0; nsing&lt;n &amp;&amp; sdiag[nsing]!=0; nsing++) {}</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160; </div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;    wa.tail(n-nsing).setZero();</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    s.topLeftCorner(nsing, nsing).transpose().template triangularView&lt;Upper&gt;().solveInPlace(wa.head(nsing));</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;  </div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    <span class="comment">// restore</span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    sdiag = s.diagonal();</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    s.diagonal() = x;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160; </div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    <span class="comment">/* permute the components of z back to components of x. */</span></div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;    x = iPerm * wa; </div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;}</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160; </div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar, <span class="keywordtype">int</span> Options_, <span class="keyword">typename</span> Index&gt;</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;<span class="keywordtype">void</span> lmqrsolv(</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;  SparseMatrix&lt;Scalar,Options_,Index&gt; &amp;s,</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;  <span class="keyword">const</span> PermutationMatrix&lt;Dynamic,Dynamic&gt; &amp;iPerm,</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;  <span class="keyword">const</span> <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt;Scalar,Dynamic,1&gt;</a> &amp;diag,</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;  <span class="keyword">const</span> <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt;Scalar,Dynamic,1&gt;</a> &amp;qtb,</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;  <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt;Scalar,Dynamic,1&gt;</a> &amp;x,</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;  <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt;Scalar,Dynamic,1&gt;</a> &amp;sdiag)</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;{</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;  <span class="comment">/* Local variables */</span></div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;  <span class="keyword">typedef</span> SparseMatrix&lt;Scalar,RowMajor,Index&gt; FactorType;</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i, j, k, l;</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    Scalar temp;</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = s.cols();</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt;Scalar,Dynamic,1&gt;</a>  wa(n);</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    JacobiRotation&lt;Scalar&gt; givens;</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160; </div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    <span class="comment">/* Function Body */</span></div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    <span class="comment">// the following will only change the lower triangular part of s, including</span></div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;    <span class="comment">// the diagonal, though the diagonal is restored afterward</span></div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160; </div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    <span class="comment">/*     copy r and (q transpose)*b to preserve input and initialize R. */</span></div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    wa = qtb;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;    FactorType R(s);</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;    <span class="comment">// Eliminate the diagonal matrix d using a givens rotation</span></div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;    <span class="keywordflow">for</span> (j = 0; j &lt; n; ++j)</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;    {</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;      <span class="comment">// Prepare the row of d to be eliminated, locating the </span></div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;      <span class="comment">// diagonal element using p from the qr factorization</span></div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;      l = iPerm.indices()(j);</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;      <span class="keywordflow">if</span> (diag(l) == Scalar(0)) </div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;        <span class="keywordflow">break</span>; </div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;      sdiag.tail(n-j).<a class="codeRef" href="../classEigen_1_1PlainObjectBase.html#acc39eaf7ba22b725c86f1b9b8bb57c3c">setZero</a>();</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;      sdiag[j] = diag[l];</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;      <span class="comment">// the transformations to eliminate the row of d</span></div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;      <span class="comment">// modify only a single element of (q transpose)*b</span></div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;      <span class="comment">// beyond the first n, which is initially zero. </span></div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;      </div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;      Scalar qtbpj = 0; </div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;      <span class="comment">// Browse the nonzero elements of row j of the upper triangular s</span></div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;      <span class="keywordflow">for</span> (k = j; k &lt; n; ++k)</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;      {</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;        <span class="keyword">typename</span> FactorType::InnerIterator itk(R,k);</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;        <span class="keywordflow">for</span> (; itk; ++itk){</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;          <span class="keywordflow">if</span> (itk.index() &lt; k) <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;          <span class="keywordflow">else</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;        }</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;        <span class="comment">//At this point, we have the diagonal element R(k,k)</span></div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;        <span class="comment">// Determine a givens rotation which eliminates </span></div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;        <span class="comment">// the appropriate element in the current row of d</span></div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;        givens.makeGivens(-itk.value(), sdiag(k));</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;        </div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;        <span class="comment">// Compute the modified diagonal element of r and </span></div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;        <span class="comment">// the modified element of ((q transpose)*b,0).</span></div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;        itk.valueRef() = givens.c() * itk.value() + givens.s() * sdiag(k);</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;        temp = givens.c() * wa(k) + givens.s() * qtbpj; </div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;        qtbpj = -givens.s() * wa(k) + givens.c() * qtbpj;</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;        wa(k) = temp;</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;        </div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;        <span class="comment">// Accumulate the transformation in the remaining k row/column of R</span></div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;        <span class="keywordflow">for</span> (++itk; itk; ++itk)</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;        {</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;          i = itk.index();</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;          temp = givens.c() *  itk.value() + givens.s() * sdiag(i);</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;          sdiag(i) = -givens.s() * itk.value() + givens.c() * sdiag(i);</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;          itk.valueRef() = temp;</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;        }</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;      }</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;    }</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;    </div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;    <span class="comment">// Solve the triangular system for z. If the system is </span></div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    <span class="comment">// singular, then obtain a least squares solution</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> nsing;</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    <span class="keywordflow">for</span>(nsing = 0; nsing&lt;n &amp;&amp; sdiag(nsing) !=0; nsing++) {}</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    </div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    wa.tail(n-nsing).setZero();</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;<span class="comment">//     x = wa; </span></div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;    wa.head(nsing) = R.topLeftCorner(nsing,nsing).template triangularView&lt;Upper&gt;().solve<span class="comment">/*InPlace*/</span>(wa.head(nsing));</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;    </div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;    sdiag = R.diagonal();</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;    <span class="comment">// Permute the components of z back to components of x</span></div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;    x = iPerm * wa; </div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;}</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160; </div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160; </div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_LMQRSOLV_H</span></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="../classEigen_1_1Matrix.html">Matrix&lt; Scalar, Dynamic, 1 &gt;</a></div></div>
<div class="ttc" id="aclassEigen_1_1PlainObjectBase_html_acc39eaf7ba22b725c86f1b9b8bb57c3c"><div class="ttname"><a href="../classEigen_1_1PlainObjectBase.html#acc39eaf7ba22b725c86f1b9b8bb57c3c">Eigen::PlainObjectBase::setZero</a></div><div class="ttdeci">Derived &amp; setZero(Index size)</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div></div>
</div><!-- fragment --></div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
  <ul>
    <li class="navelem"><a class="el" href="dir_8d80078a9d0677ffcc4e95dc0faac368.html">unsupported</a></li><li class="navelem"><a class="el" href="dir_146d0efcf5acec477a223a5f4dae5578.html">Eigen</a></li><li class="navelem"><a class="el" href="dir_32cf1c807a6a54b74f3595d5e0573479.html">src</a></li><li class="navelem"><a class="el" href="dir_e64d74fdc1defde03efbbf5c04b4c882.html">LevenbergMarquardt</a></li><li class="navelem"><b>LMqrsolv.h</b></li>
    <li class="footer">Generated on Thu Apr 21 2022 13:07:59 for Eigen-unsupported by
    <a href="http://www.doxygen.org/index.html">
    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.9.1 </li>
  </ul>
</div>
</body>
</html>
